all possible combinations of 4 numbers
For four distinct numbers, there are 24 different ways to arrange them. This comes from the permutation formula 4!=4×3×2×1=244!=4\times 3\times 2\times 1=244!=4×3×2×1=24.
Core idea
- When a question asks for “all possible combinations of 4 numbers” but means “all different orders using all 4 once each,” it is talking about permutations , not combinations.
- With 4 distinct numbers (say 1, 2, 3, 4), any of them can go in the first position (4 choices), then 3 choices remain for the second, 2 for the third, and 1 for the last, giving 4×3×2×1=244\times 3\times 2\times 1=244×3×2×1=24 total arrangements.
What the 24 look like (example 1–2–3–4)
If the four numbers are 1, 2, 3, and 4, the 24 permutations are:
- 1234, 1243, 1324, 1342, 1423, 1432
- 2134, 2143, 2314, 2341, 2413, 2431
- 3124, 3142, 3214, 3241, 3412, 3421
- 4123, 4132, 4213, 4231, 4312, 4321
Each one uses all four numbers exactly once, just in a different order.
If repeats are allowed
Sometimes “all possible combinations of 4 numbers” means 4-digit codes where digits can repeat.
- If you have 4 choices for each position (for example, digits 0, 1, 7, 9), and repeats are allowed, then there are 44=2564^4=25644=256 possible 4-digit codes.
- If you have 10 choices (digits 0–9) with repeats allowed, there are 104=10,00010^4=10{,}000104=10,000 possible 4-digit codes.
Quick reference table
| Interpretation | Rule | Number of results |
|---|---|---|
| 4 distinct numbers, each used once, order matters | $$4! = 24$$ | 24 arrangements (like 1234, 1243, …) |
| 4 possible digits, 4-digit code, repeats allowed | $$4^4$$ | 256 codes |
| Digits 0–9, 4-digit PIN, repeats allowed | $$10^4$$ | 10,000 codes |